The value of tan 100^{circ} + tan 125^{circ} | vedclass

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(D) We use the tangent addition formula: $	an(A + B) = \frac{	an A + 	an B}{1 - 	an A 	an B}$.Let $A = 100^{\circ}$ and $B = 125^{\circ}$.Then $A

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(D) We use the tangent addition formula: $	an(A + B) = \frac{	an A + 	an B}{1 - 	an A 	an B}$.Let $A = 100^{\circ}$ and $B = 125^{\circ}$.Then $A + B = 225^{\circ}$.Substituting these values into the formula:$	an(225^{\circ}) = \frac{	an 100^{\circ} + 	an 125^{\circ}}{1 - 	an 100^{\circ} 	an 125^{\circ}}$.Since $	an(225^{\circ}) = 	an(180^{\circ} + 45^{\circ}) = 	an 45^{\circ} = 1$,we have:$1 = \frac{	an 100^{\circ} + 	an 125^{\circ}}{1 - 	an 100^{\circ} 	an 125^{\circ}}$.Multiplying both sides by $(1 - 	an 100^{\circ} 	an 125^{\circ})$:$1 - 	an 100^{\circ} 	an 125^{\circ} = 	an 100^{\circ} + 	an 125^{\circ}$.Rearranging the terms:$	an 100^{\circ} + 	an 125^{\circ} + 	an 100^{\circ} 	an 125^{\circ} = 1$.

The value of $\tan 100^{\circ} + \tan 125^{\circ} + \tan 100^{\circ} \tan 125^{\circ} =$ ?

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